The synthesis of polyurethanes using extruder reactors is known to the art. Also, there are known various radiation curable polyurethanes, e.g., polyurethanes which cross link under the influence of ultraviolet or electron beam radiation. Such polymers are potentially useful in several fields, such as magnetic recording tape binders; automobile body protective coverings; wound management materials; and high moisture vapor transmission films. However, although the advantages of continuous processing in an extruder reactor (e.g., the ability to modify the polymer on line without stopping the process) are known, the necessary elevated temperature and shear conditions within an extruder have led to the belief that radiation curable functionalities such as acrylates would not survive the extrusion process.